In the related art, a method of measuring residual stress present in a specimen while applying a load to the specimen after picking up the specimen from material has been proposed and used. Particularly, a destructive method of measuring residual stress, in which a specimen is picked up from material to measure residual stress, cannot be used for the measurement of residual stress of buildings or industrial facilities which are actually in use, so that it is necessary to use a nondestructive method to measure the residual stress.
Thus, a technique of evaluating residual stress through repeatedly loading and unloading the surface of a material, measuring indentation load and depth, and measuring residual stress of the material based on the indentation load and depth has been proposed and used.
Korean Patent Registration No. 0416723, which was filed by and issued to the applicant of the present invention, disclosed “Apparatus for Measuring Residual Stress, Methods of Measuring Residual Stress and Residual Stress Data Using the Apparatus, and Recording Medium for Storing Software for the Residual Stress Measuring Method”.
The conventional apparatus and method for measuring residual stress of a material will be described herein below with reference to FIG. 1. In order to measure residual stress, an indentation load-depth curve of a reference specimen (stress-free state) is required. The reason for this is to compare an indentation load-depth curve of an actual specimen with that of the reference specimen. In order to measure residual stress, the following process must be executed, and the sequence thereof is described below.
First, continuous multiple indentation tests for the reference specimen are executed using the above-mentioned residual stress measuring apparatus. A fitted equation of a loading curve, the slope of an unloading curve, and an actual indentation depth hc are obtained based on the curves obtained from the tests.
Only loading curves which are free from mechanical relaxation, a deceleration/acceleration effect, and a creep effect are separated from the obtained indentation load-depth curves to execute a fitting process. This fitting process is required in order to accurately measure a value, because the shapes of unloading curves are distorted in the case of actual multiple indentations and so the curves are different from that of an actually applied load.
A load applied when Vickers indentation tests, indicating a certain hardness, are executed is proportional to an indentation area, but it is difficult to accept the load as being precisely proportional to the indentation area due to complicated elasticity/plastic strain under the indenter tip. Accordingly, the relationship between the indentation load and indentation depth given at the time of loading is fitted in the form of a fifth-order equation, as expressed in Equation 1, thus obtaining an experimental equation,L=a1h5+a2h4+a3h3+a4h2+a5h+c  [Equation 1]
wherein a1, a2 a3, a4, a5, and c are constants.
Next, when each unloading curve is analyzed, each unloading curve is also fitted in the form of the following Equation 2 in the same manner as the analysis of the loading curves. Equation 2 is an algorithm for calculating the curve that is closest to all points on the unloading curves,L=k(h−hf)m  [Equation 2]
where hf is a final residual depth after the load is removed. When logs are taken of both terms of Equation 2 to carry out a fitting process, k and m can be obtained, and the slope S of the unloading curve can be obtained using k and m. The relationship of the slope S to k and m is defined in the following Equation 3.
                    S        =                                            (                                                ⅆ                  L                                                  ⅆ                  h                                            )                                      h              =                              h                m                                              =                      k            ⁢                                                  ⁢                                          m                ⁡                                  (                                      h                    -                                          h                      f                                                        )                                                            m                -                1                                                                        [                  Equation          ⁢                                          ⁢          3                ]            
A real contact area between the indenter tip and the specimen is maintained while an elastic indentation load is removed, the unloading curve is linear, and a contact depth hc is determined from the linear unloading curve. However, the contact area decreases depending on the actual shape of the indenter tip while the load is removed, and elastic bending around the contact area also varies. A relationship indicating the contact between the indenter tip and the specimen can be expressed as the following Equation 4.
In Equation 3, the slope S is determined by taking a maximum displacement value on each unloading curve as hmax. After that, hmax is reset to an intersection point between the curve of the equation obtained by fitting the loading curve and a tangent line of an unloading curve which can be obtained using the slope S in each loading curve. The reason for this is to minimize error generated in the case where each unloading curve deviates from an ideal shape as a result of equipment clearance.
                              h          c                =                                            h              max                        -                          ω              ⁡                              (                                                      h                    max                                    -                                      h                    1                                                  )                                              =                                    h              max                        -                          ω              ⁢                                                          ⁢                                                L                  max                                S                                                                        [                  Equation          ⁢                                          ⁢          4                ]            
In Equation 4, hi is an intercept depth when the tangent line of the unloading curve is extended, and hmax is a maximum indentation depth in each unloading curve, obtained using the intersection point between the above loading curve and the tangent line of the unloading curve, which can be obtained using the slope S.
ω is a geometrical factor of the indenter tip and is given as 0.72 in the case of the Vickers indenter tip. Such contact depth determination is carried out for each unloading curve.
After the tests for the reference specimen have been completed, tests for specimens requiring the measurement of residual stress are carried out. In this case, there is no need to execute a partial load removing step, which is due to the fact that, since the relative difference between applied loads with respect to a certain indentation depth at each specimen is directly related to residual stress in each specimen, it is not necessary to obtain a value hc after a standardized indentation depth hc has been previously obtained from the reference specimen.
After continuous indentation tests have been carried out for specimens requiring the measurement of residual stress, a fitting procedure for a loading curve is executed in the same manner as that described for the reference specimen tests. An equation obtained through the fitting procedure is compared with the fitted equation obtained from the reference specimen. In this case, the sign of residual stress in each specimen can be determined through the shape of a measured indentation load-depth curve. That is, if the measured indentation load-depth curve is placed above that of the reference specimen, it can be determined that compressive residual stress exists; otherwise it can be determined that tensile residual stress exists.
After loading curve equations are obtained, residual stress is measured by relationships, which will be described later. It can be considered that the difference between indentation loads applied to the reference specimen and an actual specimen at the same indention depth is generated due to residual stress, so residual stress can be obtained by dividing the load difference by a real contact area. In this embodiment, the load difference was obtained at the indentation depth hmax obtained from each unloading curve. Therefore, in a single test, a number of calculated residual stress values equal to the number of partial unloading times, obtained during the reference test, can be obtained.
A constant α exists because the distribution states of stresses present in the specimen are different, for example, in the case of a hydrostatic biaxial stressed state (σx=σy) on a thin film, or in the case where only a single directional stress is considered to be important (σx>>σy) like a weldment.
If the influence due to residual stress is indicated by a difference in an applied load at the same indentation depth, the stress value at that time can be expressed by the following Equation 5 because the stress value is obtained by dividing the applied load by a unit area,
                                          L            res                    =                      L            -                          L              o                                      ⁢                                  ⁢                              σ            res                    =                      α            ⁢                                                  ⁢                                          L                res                                            A                c                                                                        [                  Equaiton          ⁢                                          ⁢          5                ]            
where Lres=L0−L=ΔL
where L is an indentation load applied to the actual specimen, L0 is an indentation load applied to the reference specimen, and Ac is a real contact area and is expressed as the following Equation 6 in consideration of the geometrical form of a Vickers indenter tip.Ac=24.5hc2  [Equation 6]
If each value Ac obtained by applying each hc, obtained from the reference specimen to Equation 6, is applied to Equation 5, actual residual stress values vary within a predetermined range, which is due to the fact that, as the indentation load increases, the plastic area under the indenter tip increases.
Accordingly, residual stress is defined by the mean value obtained by averaging residual stress values corresponding to contact areas.
However, in the conventional method of measuring residual stress, a minute error may occur due to the difference between the ideal value obtained from ideal measurement and the actual value obtained from an actual test. In other words, when a graph having ideal indentation load-depth curves cannot be obtained, the indentation load may be underestimated or the displacement may be overestimated, so that an error may be generated.
Furthermore, in the related art, the slope of an unloading curve is obtained from the continuous indentation load-depth curve and is used to measure residual stress. However, a substantial error may occur between an ideal unloading curve and an actual unloading curve, so that it is necessary to eliminate the error.
In addition, the relationship between an applied indentation load with respect to a certain indentation depth while loading is appropriately converted from a complex fifth-order equation into a simple second-order equation which can generate a curve that agrees with an actual indentation curve. Furthermore, the conventional method of measuring residual stress cannot account for an error caused by a blunted tip, which has become blunt due to repeated tests, or by pile-up or sink-in of a material, so that measuring results may include an error. Thus, it is required to compensate for the error.
In addition, it is impossible to estimate a stress-free curve of an actual weldment in the stress-free state, so that an error may occur in the measuring results and must be compensated for.
In the related art, a stress-free curve can be obtained only from a reference specimen (stress-free state). It is impossible to adapt the stress-free curve to a specified region, such as a weldment, which has stresses acting in different directions or having different sizes. To obtain a stress-free curve, a stress-free state must be produced through mechanical or thermal techniques prior to measurement. In other words, a stress-free curve cannot be estimated from an actual weldment in a stress-free state, so that, if a stress-free curve is estimated from a material exhibiting an anisotropic stressed state in a weldment, an error may occur in measuring results and must be compensated for.